3D rupture effects (seismogenic depth) Huihui Weng Jean-Paul - PowerPoint PPT Presentation

3D rupture effects (seismogenic depth) Huihui Weng Jean-Paul Ampuero ICTP, Trieste, Italy, 2-14 Sep.

Rupture speeds in 2D Modes II (strike slip) Supershear Sub-Rayleigh v R v S v E v P Rupture speed Unstable Modes III (dip slip) Subshear Rupture speed v S

Stable speeds in 2D Modes II (strike slip) velocity term g(v) for energy release rate Supershear Sub-Rayleigh v R v S v E v P Rupture speed Unstable Modes III (dip slip) Subshear Rupture speed v S

Finite seismogenic width h h c c n n e e r r T T Aseismic stable Aseismic stable S S u u b b d d u u c c t t i i n n g g p p l l a a c c e e Aseismic stable Aseismic stable Seismogenic Zone Weng and Ampuero, 2019 Fault and Rock Mechanics (FARM)

Elongated earthquake ruptures 2004 Mw 9.3 Sumatra >10 10 2004 Mw 6 Parkfield SRCMOD Wells and Coppersmith, 1994 8 Henry and Das, 2001 Strike-slip Dip-slip 6 L / W 4 2 Ma et al 2008 0 3 4 5 6 7 8 9 10 M w Ishii et al 2005

Elongated earthquake ruptures Galis et al 2018

overview • Equation of motion for mode III in 3D • Equation of motion for mode II in 3D -- Subshear -- Supershear • Ruptures of mixture of modes II and III

overview • Equation of motion for mode III in 3D • Equation of motion for mode II in 3D -- Subshear -- Supershear • Ruptures of mixture of modes II and III

Warm-ups Kinematics Dynamics http://sdsu-physics.org sciencenotes.org F = ma Newton’s second law

Slip inversion method Ide, 1997

Imaged by back-projection • Track rupture speed • High frequency data • Seismic array Meng et al. (2016) Hutko (2009)

Questions • How to explain observed source kinematics? • What is the intrinsic earthquake physics ? • How to link kinematics and dynamics of earthquakes?

Fracture mechanics: -- connection between kinematics and dynamics

Linear elastic fracture mechanics Ø Energy balance between energy release rate and fracture energy Ø Rupture speed as a function of distance Kostrov, Freund, Andrews (60-70s)

Linear elastic fracture mechanics K I Kostrov, Freund, Andrews (60-70s)

Linear elastic fracture mechanics K I Kostrov, Freund, Andrews (60-70s)

Linear elastic fracture mechanics • Classical LEFM is not “inertial” • Speed is independent of acceleration Jump of fracture enregy G c L Response immediately v r Infinite acceleration L

Crack in bounded media Waves are reflected back Marder (1998) Ø Release elastic energy is linearly proportional to width of strip LEFM Ø

Strip experiments Livne et al 2008 Goldman et al 2010

Inertial equation of motion

Inertial equation of motion Force? Apparent mess? Acceleration F = ma

Key points 1 Classical LEFM links kinematics and dynamics of 2D infinite media, which is not “inertial” 2 The crack-tip-equation-of-motion for 2D strip media is “inertial” Which may control ruptures on 3D bounded fault? 1 or 2 ?

The dynamics of elongated ruptures : -- Rupture acceleration (how rupture begins?) -- Rupture deceleration (how rupture stops?)

Analytical model W Ingredients • Anti-plane fault embed in 3D full-space • Uniform elastic properties • Uniform fault parameters • Uniform seismogenic width • Steady-state speed

Analytical model (3 equations) x 1 x 2 x 3 Aseismic region Aseismic region e l i f o r Aseismic region Aseismic region p p i l S Seismogenic width W

Analytical model (3 equations) x 1 Reduce to 1 equation x 2 x 3 Aseismic region Aseismic region e l i f o r Aseismic region Aseismic region p p i l S Seismogenic width W

Analytical model (3 equations) x 1 Reduce to 1 equation x 2 x 3 Aseismic region Aseismic region Sin(k 3 x 3 ) Slip profile Slip approximation Aseismic region Aseismic region Seismogenic width W

Analytical model (3 equations) x 1 Reduce to 1 equation x 2 x 3 Aseismic region Aseismic region Sin(k 3 x 3 ) Slip profile Slip approximation Aseismic region Aseismic region Seismogenic width W

Energy release rate ü Energy release rate G is a constant independent of rupture s peed and distance, i.e., G = G 0 ü G c = G 0 à propagate at any speed G c ≠ G 0 ?

Energy balance at rupture tip Intuitive physical process • G 0 = G c à ruptures propagate steadily • G 0 > G c à ruptures accelerate ↑ • G 0 < G c à ruptures decelerate ↓ edennyweb.wordpress.com

Validation from numerical simulations τ τ s τ 0 d 0 τ d d

Rupture acceleration • G 0 > G c à ruptures accelerate ↑ • G c / G 0 plays an important role in controlling rupture speed 1.0 a 0.8 Energy ratio decreases 0.6 v r / v s 2.5D simulations 0.4 G c / G 0 0.99 0.93 · 0.98 0.92 0.2 0.97 0.9 0.96 0.8 0.95 0.7 0.94 0.6 0.0 0 5 10 15 20 L / W Weng and Ampuero, 2019

Rupture acceleration • G 0 > G c à ruptures accelerate ↑ • G c / G 0 plays an important role in controlling rupture speed 1.0 a 0.8 Energy ratio decreases 0.6 v r / v s 2.5D simulations 0.4 G c / G 0 0.99 0.93 · 0.98 0.92 0.2 0.97 0.9 0.96 0.8 0.95 0.7 0.94 0.6 0.0 0 5 10 15 20 L / W Weng and Ampuero, 2019

Rupture acceleration • G 0 > G c à ruptures accelerate ↑ • G c / G 0 plays an important role in controlling rupture speed 1.0 a 0.8 Energy ratio decreases 0.6 v r / v s 2.5D simulations 0.4 G c / G 0 0.99 0.93 · 0.98 0.92 0.2 0.97 0.9 0.96 0.8 0.95 0.7 0.94 0.6 0.0 0 5 10 15 20 L / W Weng and Ampuero, 2019

Rupture acceleration • G 0 > G c à ruptures accelerate ↑ • G c / G 0 plays an important role in controlling rupture speed 1.0 a b 3 A = π and P = 3 0.8 2 / (1 - G c / G 0 ) 2 0.6 v r / v s 2.5D simulations v r W / v s 0.4 1 G c / G 0 0.99 0.93 · 0.98 0.92 0.2 0.97 0.9 0.96 0.8 0.95 0.7 0.94 0.6 0.0 0 0 5 10 15 20 0.0 0.2 0.4 0.6 0.8 1.0 L / W v r / v s Weng and Ampuero, 2019

Rupture deceleration • G 0 < G c à ruptures decelerate ↓ • Starting speed also plays a role • Larger rupture speed lead to longer distance a 1.0 G c / G 0 1.01 1.05 1.02 1.06 0.8 1.03 1.07 1.04 1.08 0.6 v r / v s v / v 0.4 · 0.2 G c / G 0 = 0.9 0.0 0 10 20 L / W 2.5D simulations Weng and Ampuero, 2019

Rupture deceleration • G 0 < G c à ruptures decelerate ↓ • Starting speed also plays a role • Larger rupture speed lead to longer distance a 1.0 G c / G 0 1.01 1.05 1.02 1.06 0.8 1.03 1.07 1.04 1.08 0.6 v r / v s v / v 0.4 · 0.2 G c / G 0 = 0.9 0.0 0 10 20 L / W 2.5D simulations Weng and Ampuero, 2019

Rupture deceleration • G 0 < G c à ruptures decelerate ↓ • Starting speed also plays a role • Larger rupture speed lead to longer distance c a 1.0 4 G c / G 0 A = 1.2 π 1.01 1.05 1.02 1.06 0.8 1.03 1.07 P = 2.6 1.04 1.08 3 2 / (1- G c /G 0 ) 0.6 v r / v s v / v 2 0.4 v r W / v s · · 1 0.2 G c / G 0 = 0.9 0.0 0 0 10 20 0.0 0.2 0.4 0.6 0.8 1.0 L / W v r / v s 2.5D simulations Weng and Ampuero, 2019

Validation from 3D simulations 1.0 1.0 A = 1.2 π P = 2.6 0.8 0.8 Rupture speed Rupture speed 0.6 0.6 A = π and P = 3 v r / v s v r / v s 0.4 0.4 G c / G 0 0.97 G c / G 0 0.88 0.2 0.2 0.95 0.84 1.03 1.08 0.92 0.7 1.04 1.1 0.9 0.6 1.06 Theoretical curves Theoretical curves 0.0 0.0 0 5 10 0 5 10 L / W Distance L / W Distance Weng and Ampuero, 2019

“Inertial” rupture asperity barrier a 1.0 b 0.2 0.8 0.6 0.1 2 v r / v s v r W / v s 0.4 · Acceleration 0.0 Deceleration 0.2 −0.1 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0 10 20 30 40 v r / v s L / W • Rupture evolution predicted by rupture-tip-equation-of-motion • Rupture is also “inertial” Weng and Ampuero, 2019

Elongated ruptures in the lab

Key points 1 Closed-form energy release rate on 3D bounded fault is a constant: 2 Ruptures on 3D bounded fault are controlled by the theoretical equation for very long ruptures:

Implications: -- Rupture potential and final earthquake size -- Super-cycle

Rupture potential Propagation direction R 1 R 3 G 0 G c R 4 R 2 2 3 4 1 asperity barrier asperity barrier

Rupture potential Propagation direction R 1 R 3 G 0 “Kinetic” energy? “Potential” energy? G c R 4 R 2 2 3 4 1 asperity barrier asperity barrier

Rupture potential Propagation direction R 1 R 3 G 0 “Kinetic” energy? “Potential” energy? G c R 4 R 2 Rupture potential 2 3 4 1 asperity barrier asperity barrier

Determine earthquake size A(1-G c /G 0 ) Along strike 0 Rupture potential φ(x) Gravity potential Weng and Ampuero, JGR, in revision www.thinglink.com

Determine earthquake size A(1-G c /G 0 ) Along strike 0 Rupture potential φ(x) Gravity potential Weng and Ampuero, 2019 www.thinglink.com

Determine earthquake size A(1-G c /G 0 ) Along strike 0 Rupture potential φ(x) Gravity potential Weng and Ampuero, 2019 www.thinglink.com

Super earthquake cycles? Ø Fault segmentation Ø Maximum magnitude? Villegas-Lanza et al., (2016)